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Global properties of invariant measures. (English) Zbl 1131.35318
Summary: We study global regularity properties of invariant measures associated with second order differential operators in \(\mathbb{R}^N\). Under suitable conditions, we prove global boundedness of the density, Sobolev regularity, a Harnack inequality and pointwise upper and lower bounds.

MSC:
35J15 Second-order elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
35J45 Systems of elliptic equations, general (MSC2000)
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
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